Lemma 2.4 ([1]}) 
There is a unique ring map \(D_\sigma :A \rightarrow W(A)\)  making the following diagram commute for each \(i \ge 0\) :
\(\begin{tikzcd}A [r,"D_\sigma "] [dr,"\sigma ^i"^{\prime }] & W(A) [d,"w_i"] \\& A\end{tikzcd}\) 

